Optical processor architecture

ABSTRACT

Apparatus for optically applying a transform to data, comprising: a spatially modulated light source, that generates a spatially modulated light beam; a diffractive element that replicates said light beam; and a lens that applies a Fourier transform to said replicated light beam.

RELATED APPLICATIONS

This application is a Divisional filing of U.S. application Ser. No.09/979,183, filed on Jul. 15, 2002 which is a U.S. national filing ofPCT Application No. PCT/IL00/00283, filed on May 19, 2000, which is acontinuation-in-part of U.S. application Ser. No. 09/926,547, filed onMar. 5, 2002 which is a U.S. national filing of PCT Application No.PCT/IL99/00479, filed on Sep. 5, 1999, the disclosures of all of whichare incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to the field of optical processorarchitectures

BACKGROUND OF THE INVENTION

A general linear transformation (GLT) in its discrete form is defined byits kernel function W. The transformed function G as a function of a twodimensional input g(x,y) is thus:G(ξ, η)=ΣΣg(x,y)W(x, y; ξ, η)  (1)

For a two dimensional object having the size of 1000 by 1000 pixels, ageneral linear transformation requires 10¹² multiplications.

The equation (1) for a one dimensional vector is:G(ξ)=Σg(x)W(x; ξ)  (2)

In matrix formulation, equation (2) becomes $\begin{matrix}{\begin{bmatrix}G_{1} \\G_{2} \\\vdots \\\vdots \\G_{N}\end{bmatrix} = {\begin{bmatrix}g_{1} & g_{2} & \cdots & \cdots & g_{N}\end{bmatrix} \cdot \begin{bmatrix}W_{11} & W_{12} & \cdots & \cdots & W_{1N} \\W_{21} & W_{22} & \quad & \quad & \vdots \\\vdots & \quad & ⋰ & \quad & \vdots \\\vdots & \quad & \quad & ⋰ & \vdots \\W_{N1} & \cdots & \cdots & \cdots & W_{NN}\end{bmatrix}}} & (3)\end{matrix}$, showing that a GLT can be performed as a vector-matrix multiplication.

Dammann gratings are described, for example in “High Efficiency In-LineMultiple Imaging by Means of Multiple Phase Holograms”, H. Damman, K.Gortler, Optics communications, 3(5), 321-315

The following is a partial list of publications that describe one ormore of optical processing methods, optical processors and cross-barswitches: For example: “Cosinusoidal transforms in white light,” by N.George and S. Wang, in Applied Optics, Vol. 23, No 6, 1984; “Hartleytransforms in hybrid pattern matching,” by Nomura, K. Itoh and Y.Ichioka, in Applied Optics, Vol. 29, No. 29, 1990; “Lens design for awhite light cosine transform achromat,” by K. B. Farr and S. Wang, inApplied Optics, Vol. 34, No. 1, 1995; “Optical computing,” by Feitelsonin a chapter titled, “Optical image and signal processing,” pp. 102-104(general discrete linear transforms using lenslet array) and pp. 117-129(which describe matrix multiplication), MIT press 1988; “Opticalcrossbar interconnected digital signal processor with basic algorithms,”by A. D. McAulay, in Optical engineering, Vol. 25, P. 25, 1986;“Historical perspectives: Optical crossbars and optical computing,” byR. Arrathoon, in Proc. SPIE, Vol. 752, P. 2, 1987; “Optoelectronicparallel computing system with optical image crossbar switch,” by M.Fukui, in Applied Optics 32, 6475-6481, 1993; “Optical crossbar elementsused for switching networks,” by Y. Wu, L. Liu and Z. Wang, in AppliedOptics, Vol. 33, No. 2, 175-178, 1994; “Implementation of an opticalcrossbar network based on directional switches,” by KH. Brenner and T.M. Merklein, in Applied Optics, Vol. 31, No. 14, 2446-2451, 1992; “Fullyparallel, high-speed incoherent optical method for performing discreteFourier transforms,” by J. W. Goodman, A. R. Dias and L. M. Woody, inOptics Letters, Vol. 2, No. 1, 1-3, 1978; “High throughput optical imagecrossbar switch that uses a point light source array,” by M. Fukui andK. Hitayama, Optics Letters, Vol. 18, No. 5, 376-378, 1993; “Performanceof 4×4 optical crossbar switch utilising acousto optic deflector,” by P.C. Huang, W. E. Stephens. C. Banwell, and L. A. Reith, ElectronicsLetters, Vol. 25, No.4, 252-253, 1989; “Link analysis of a deformablemirror device based optical crossbar switch,” by R. W. Cohn, OpticalEngineering Vol. 31, No. 1, 134-140, 1992; “Compact optical crossbarswitch,” S. Reinhorn, Y. Amitai, A. A. Friesem, A. W. Lohmann and S.Gorodeisky, Applied Optics, Vol. 36, No. 5, 1039-1044, 1997; “Microlensarray processor with programmable weight mask and direct optical input,”by V. Schmid, E. Lueder, G. Bader, G. Maier and J. Siegordner, Proc.SPIE Vol. 3715, 175-184, 1999; and European patent applicationpublication 0577258 by Nakajima et. al. entitled: “Picture compressingand restoring system and record pattern forming method for a spatiallight modulator.” The disclosures of all of the above publications areincorporated herein by reference.

SUMMARY OF THE INVENTION

An aspect of some embodiments of the invention relates to using adiffractive optical replicator, for example a Dammann grid, or a Ronchigrating to replicate a light source. The replicated light source may beused, for example, to perform a DCT transform using a Fouriertransforming system. In one exemplary embodiment, the light sourcecomprises an array of VCELs or an SLM image. The replicated light istransformed using a lenslet array and the transformed light is detectedby a photo-electric detector.

An aspect of some embodiments of the invention relates to applying atransform to a linear one dimensional source, by spreading the source ina direction perpendicular to the extent of the light source andoptically processing the spread light. In one embodiment, the source,for example a one-dimensional array of VCELs is spread using a lens or areflector, such as a parabolic reflector. In another embodiment, thesource is spread using non-imaging optics, for example light guides.

In some embodiments of the invention the light source is spatiallyand/or temporally coherent. In other embodiments, an incoherent lightsource is used. Also, instead of electro-optical detection, in someembodiments the transformed light is used for further processing,optionally being detected by an array of optical fibers or by a lens orlenslet array.

There is thus provided in accordance with an exemplary embodiment of theinvention, apparatus for optically applying a transform to data,comprising:

-   -   a spatially modulated light source, that generates a spatially        modulated light beam encoding said data by said modulation;    -   a diffractive element that replicates said light beam; and    -   a lens that applies a Fourier transform to said replicated light        beam. Optionally, the apparatus comprises a detector that        detects said transformed light. Optionally, the apparatus        comprises electronic circuitry that converts said detected        signals into a discrete transform of said data. Optionally, said        transform is a linear transform. Optionally, said transform is a        DCT transform.

In an exemplary embodiment of the invention, said replicating comprisesreplicating said beam to a two dimensional arrangement. Alternatively oradditionally, said diffractive element comprises a Dammann grating.Alternatively, said diffractive element comprises a Ronchi grid.

There is also provided in accordance with an exemplary embodiment of theinvention, apparatus for optically applying an transform to data,comprising:

-   -   a linear array of light sources;    -   at least one first optical element for converting light from        said arrays into a two dimensional array of light, wherein each        light source is a line in said two dimensional array of light;    -   at least one transforming optical element that applies a        transform to said spread light; and    -   at least one second optical element that combines said        transformed spread light onto a linear detector array,    -   wherein said first optical element is one of reflective,        anamorphic or non-imaging. Optionally, said first optical        element is an anamorphic cylindrical lens having different focal        lengths in two directions. Alternatively, said first optical        element is an anamorphic reflector having different focal        lengths in two directions. Alternatively, said first optical        element is a curved reflector. Optionally, said first optical        element is a parabolic reflector. Alternatively or additionally,        said first optical element comprises a non-imaging optics        element. Optionally, said first optical element comprises a        leaky light guide.

In an exemplary embodiment of the invention, said second optical elementcomprises a lens. Optionally, said second optical element comprises ananamorphic lens.

In an exemplary embodiment of the invention, said second optical elementcomprises a reflector.

In an exemplary embodiment of the invention, said second optical elementcomprises a non-imaging optics light collector.

In an exemplary embodiment of the invention, said first optical elementcomprises an array of light guiding slabs. Alternatively oradditionally, said transforming optical element comprises a mask.Alternatively or additionally, said transforming optical elementcomprises an SLM (spatial light modulator). Alternatively oradditionally, said transforming optical element comprises a lensletarray. Alternatively or additionally, said detector is an electro-opticdetector.

BRIEF DESCRIPTION OF THE FIGURES

Some embodiments of the present invention will be now be described inthe following detailed description and with reference to the attacheddrawings, in which:

FIG. 1 is a general flowchart showing a processing method in accordancewith an exemplary embodiment of the invention;

FIG. 2 is a general flowchart showing a fan-out and fan-in section ofthe method of FIG. 1;

FIG. 3 is a schematic flowchart of a combined optical and electronicprocessing method in accordance with an exemplary embodiment of theinvention;

FIG. 4 is a schematic diagram of an optical processing system using aDammann grating in accordance with an exemplary embodiment of theinvention;

FIGS. 5A and 5B are a top and a side schematic views of a linear sourceoptical processing system in accordance with an exemplary embodiment ofthe invention;

FIGS. 6A and 6B are a top and a side schematic views of a non-imagingoptics optical processing system in accordance with an exemplaryembodiment of the invention; and

FIG. 7 is a schematic view of a two dimensional optical processingsystem, in accordance with an exemplary embodiment of the invention.

DETAILED DESCRIPTION OF SOME EMBODIMENTS

FIG. 1 is a general flowchart 100 showing a processing method inaccordance with an exemplary embodiment of the invention. Stored data(102) is transferred to a processor (104), processed, preferablyoptically (106), transferred back to a memory (108) and stored again(110).

In accordance with some embodiments of the invention, optical means areused to parallelize the processing (106). FIG. 2 is a general flowchart200 showing a fan-in and fan-out section of the method of FIG. 1. Manyprocesses can be made parallel by fanning out the input (202),processing the fanned-out input in parallel (204) and the collating theresults (fan in 206). In particular, a GLT can be performed as aplurality of simultaneous multiplications of various elements, followedby adding together of the multiplication results. In some exemplaryembodiments of the invention, optical means are used to provideefficient fan in or fan out mechanisms.

FIG. 3 is a schematic flowchart 300 of a combined optical and electronicprocessing method in accordance with an exemplary embodiment of theinvention. Prior to any optical processing, electronic preprocessing maybe performed (302), for example to perform calculations more efficientlycarried out electronically, calculations that utilize existing hardware,to match the data to the processing system and/or the processing to beperformed and/or to prepare the data for parallel processing. However,in some embodiments, no pre-processing is performed, for example, anoptical input image may be directly optically processed. The electronicdata is then converted to an optical representation (304), for exampleusing an SLM or an array of individually controllable light sources. Thelight is then optically processed (306), using various means, such aslens, holograms, SLMs, masks and/or lenslet arrays. The processed lightmay be directly utilized, for example in optical communications systemsor for displaying or printing an image. Alternatively or additionally,the light is detected (308), for example using a CCD. Optionally, thedetected signals are further electronically processed (310), for exampleto perform addition or other post processing more conveniently carriedout using electrical circuitry. Alternatively or additionally, thedetected signals are provided to an electronic circuitry.

In an exemplary application of the invention, a linear transformimplemented is a Fourier based transform, for example JPEG-DCT. However,the following described optical processor architectures may be used forother linear transforms as well and/or for processing, such asswitching, error correction and signal compression, for example using aID wavelet transform. Alternatively or additionally, non-lineartransforms and processing may also use a similar architecture orelements from the architectures described herein.

GLT can be used in many fields, including, for example, imagecompression, image enhancement, pattern recognition, signalidentification, signal compression, optical interconnects and crossbarsystems, morphologic operations, logical operations, image and signaltransformation and modeling neural networks.

Although not required, in some embodiments of the invention, the inputdata set is processed as a series of bit planes, with the results of thetransform of each bit plane being added together to yield the requiredtransform of the input data. The following equation describes therelationship between the Fourier transforming of bit plane separated andunseparated data:${F\left( {\sum\limits_{i}{2^{i}a_{i}}} \right)} = {\sum\limits_{i}{2^{i}{F\left( a_{i} \right)}}}$

This equation is correct for all linear transformations and enablestranslation of a gray level (with M gray levels) linear transformationto a set of log₂M transforms of binary input data. It should be notedthat in many cases, modulation of binary signals provides fasteroperation rates and better performance.

FIG. 4 is a schematic diagram of an optical processing system 400 usinga Dammann grating 408 for image replication, in accordance with anexemplary embodiment of the invention. Alternatively, other diffractiveelements may be used for replication, for example a Ronchi grating. Theinput source is a one or two dimensional array 404, which can be forexample, a VCSEL array, a LED array, a laser array, and/or a lightsource combined with a spatial light modulator (SLM), for example,acousto-optic, liquid crystal, mechanical or MQW (multi quantum wells)modulators.

In an exemplary embodiment an 8 by 8 array of light sources is used forarray source 404. Driver circuitry 402, which is typically electronic,but may also be of other types, such as optical, drives array source 404in correspondence with the input data to system 400.

The image on array 404 is collimated a lens 406 and replicated by areplicating structure, for example a Dammann grating 408. The replicatedimages are then processed, for example using a masking convolution orusing a lenslet array. One example of a masking convolution uses a maskarray 410. Th results of the processing are optionally collected, forexample using a lenslet array 412 onto an array of detectors 414. Thesignals generated by the detectors may be further processed by circuitry416. Array 410 can be a standard half-tone mask or it may be a grayscale mask. A passive element may be used. Alternatively, an activelycontrollable element, such as an SLM (spatial light modulator) may beused. Although a linear response mask is preferred, in some embodiments,a non-linear response mask is used instead. Also it is noted that insome uses, such as JPEG image compression, not all the coefficients arestrictly required, so they may be omitted from the mask.

A potential advantage of a Dammann grating is that the replication isalmost identical to the original even if the input illumination is notuniform. A potential advantage of VCSELs is that even though each one ofthe sources is coherent, the sources are not coherent betweenthemselves, so there may be fewer interference effects. However, neithera Darnmann grating nor a VCSEL are strictly required and they may bereplaced by other elements, in accordance with some embodiments of theinvention.

Typically, the GLT function W(x,y;ξ,η) to be performed is determined bymasks 410 and/or lenslet array 412. Although fixed masks 410 may beused, in some embodiments of the invention, masks 410 are controllable,for example being SLMs, binary or gray level.

An analysis of an exemplary system 400 is as follows:

The imaging relation of the main lens provides:${{\frac{1}{u} + \frac{1}{v}} = \frac{1}{f}},$where U is the distance between array source 404 and lens 406 and v isthe distance between Dammann grating 408 and mask array 410.

The magnification ratio is: $M = \frac{u}{v}$

The resolution condition:${2.44\lambda\quad f_{\#}} < \frac{250\quad{\mu m}}{M}$when 250 μm is the pitch of the laser sources (in other embodiments, adifferent pitch may be available). A field of view (FOV) restriction inorder to avoid spherical lens distortions may be applied as:${F\quad O\quad V} = {\frac{\Delta\quad x}{v} < {0.8\quad\lbrack{rad}\rbrack}}$where Δx is the transaxial extent of detector array 414. Although system400 is not rectangular, in some embodiments, it may be. Optionally, areflective optical element is used to fold optical paths and/or shortenthe system.

A volume V restriction condition may be defined, for example arbitrarilyrequiring a volume of less than 4000 cubic mm:V=(u+v)·[max{Δx,D}] ²<4000 [mm ³]where D is the diameter of the lens.

A cross talk condition can be defined as the interference between twoneighbored replica:${2.44\lambda\quad{f_{\#} \cdot 20}} < {a \cdot \quad\frac{250\quad{\mu m}}{M}}$where “a” is the required separation ratio between replica and 20 is anempirical constant. The “a” ratio may be extracted from this equation,assuming that each block is 8×8 pixels in size:${\Delta\quad x} = {2{a \cdot 8 \cdot 8}\frac{250\quad{\mu m}}{M}}$

In a particular implementation f=8 mm, f#=1, the light wavelength is 1μm and M=5, a following setup configuration can be achieved:

-   -   Δx=6.4 mm    -   v=9.6 mm, u=48 mm    -   FOV=38 [deg].    -   V=3686.4 [mm³]

In another particular implementation: M=4, f=8 mm, f#=1, and the lightwavelength is 1 μm. Resulting in:

-   -   Δx=8 mm    -   v=10 mm, u=40 mm    -   FOV=46 [deg].    -   V=3200 [mm³]

In some embodiments, the Dammann grating is a multi channel Dammanngrating that replicates block portions of the input image, rather thanthe entire input image as a whole, which may be associated with alenslet array instead of lens 406, for implementing a multi-channelsystem.

Another potential advantage of using a diffractive element is that aspatial shifting of the output can be achieved by varying the inputwavelength. In one exemplary embodiment, a tunable laser input is used,with different wavelengths being used for different output positionsand/or scales. Alternatively or additionally, a wavelength responsivereflector, lens or additional optical element may be used to shift theresults for different wavelengths. Other wavelength shifting techniquescan be used as well, for example, very fast modulators in combinationwith sensitive detection systems.

FIGS. 5A and 5B are a top and a side schematic views of a linear sourceoptical processing system 500 in accordance with an exemplary embodimentof the invention.

In system 500, a linear light source 504, for example an array of VCSELsis driven by electronic circuitry 502 to generate a one dimensionalpattern. Although a discrete source array is shown, in some embodiments,a continuous source array may be provided. It should be noted thatalthough a straight one dimensional source is shown, the source may alsobe curved and/or folded with corresponding changes in other elementsand/or their positioning. Alternatively, other methods of providing aone-dimensional light source may be provided. The spatially modulatedlight is spread in a transaxial direction by at least one lens 506, forexample a single cylindrical lens. Optionally, the lens is an anamorphiclens, with different focal lengths for its two axes. The spread light isthen processed by a two dimensional optical element 510, for example anarray of masks. Alternatively or additionally, an active element may beused instead, for example an LCD or other type of light valve array. Asecond lens system 512, also optionally anamorphic collects the lightonto a linear detector array 514, which is, for example, perpendicularto source array 504, so that it collects processed light from all of thesources together. Optional post processing may be performed by aprocessor 516 connected to detectors 514. The arrays may be, forexample, 64 element long, to support an 8×8 block operation.

One possibly restriction of system 500 is generated by the resolutionavailable in the Fourier plane. Assume a 256 gray level transformationmask 510 with a spatial production resolution of δ=0.5 μm. Then, thesize of each pixel in the transformation mask ought to be: δL=δ{squareroot}{square root over (256)}=0.5 μg·16=8 [cm]

This size typically defines the maximal resolution in the Fourier plane.Such a resolution requires:$\frac{\lambda\quad f}{{64 \cdot \delta}\quad x} = {\delta\quad L}$where δox is the size of the VCSEL cell and f is the lens focal length.

In an exemplary embodiment of system 500, using a VCSEL vector of 64pixels, δx=50 μm and λ=1 μm (the wavelength of the light):

-   f=50·64·8 μm=2.56 [cm]    resulting in a system length of 4f=10.24 [m]. If a f#=1 lens is    used, a lens aperture of    $D = {\frac{f}{f_{\#}} = {2.56\quad\lbrack{cm}\rbrack}}$    is obtained. A typical volume V of this exemplary system is:    V=(4f)·D ²=10.24·(2.56)²=6710 [mm ³]

It should be noted that in this and other exemplary estimatedmeasurements, different manufacturing and/or design constrains willyield different results.

FIGS. 6A and 6B are a top and a side schematic views of a non-imagingoptics optical processing system 600 in accordance with an exemplaryembodiment of the invention. System 600 is characterized in that thelight from a point source is spread using non-imaging means.

In system 600, an array of point sources 604, driven by circuitry isspread by non-imaging means, for example an array of planar light guides606, which widen from a point to a line. Optionally, the use of lightguides prevents or reduces cross-talk between channels. Alternatively,other means, such as mirrors or diffuse reflectors, may be used. Lightsources 604 may be behind the effective linear source or they may be ata different angle, for example to the side. In one embodiment, the lightis spread by scattering along a light guide to outside of the lightguide. In another example, the light is conveyed along a light guideusing total internal reflections, and exists the light guide via adiffraction grating or other non-uniformity of the surface. In aparticular embodiment of the invention, each of light guides 606comprises a distorted parabolic reflector, with a light source 604 solocated in it that the light from the source is reflected by thereflector to extend the entire width of the light guide, at its end. Inone dimension, the parabolic reflector generates a parallel beam oflight from a point source placed in its focal point, so that the lightdoes not exit the light guide. In some embodiments, no physical lightguide is provided beyond a parabolic or other design reflector. Theexpansion of light in the other dimension may be supported by adistortion of the parabola or by using other suitable curves as known inthe art of light reflecting. Alternatively or additionally, non-imagingoptics techniques are used to spread the light, for example a suitablydesigned light guide. It should be noted that parabolic or otherreflectors may also be used in conjunction with the embodiment of FIGS.5A and 5B, for example for light collection.

Light exiting from light guides 606 is processed by an optical element610, for example a mask or an SLM. The results of the processing arecollected by a second set of light guides 612, to an array 614 ofdetectors. Alternatively, a lens may be used to collect the processedlight. Optionally, a diffuser is placed adjacent element 610, to assistin imaging the processed light. In an alternative embodiment (alsosuitable for system 500) detectors 614 may be an array of lineardetectors, for example, each element having a length equal to the widthof the system. Alternatively or additionally, the light sources may bean array of linear light sources.

A potential advantage of not having imaging elements is that theresulting system may be more robust.

In an exemplary parametric design, if IL_(FOV) denotes the illuminationfield of view of the light source, then:$\Delta_{y} = {{2y_{0}} = {2 \cdot \frac{1}{4p}}}$where Δy is the width of the optical processor. Assuming that δ is thesize of the VCSEL:${p\left( {64 \cdot \delta} \right)} = {\tan\left( \frac{{IL}_{FOV}}{4} \right)}$Thus:$\Delta_{y} = \frac{64 \cdot \delta}{2\quad{\tan\left( \frac{{IL}_{FOV}}{4} \right)}}$

For an exemplary IL_(FOV) of 30 degrees and δ250 μm, a value of Δy=60 mmis obtain. An approximate volume for such an element is:V=(64·ε)²Δ_(y)=15.5 [cm ³]

FIG. 7 is a schematic view of a two dimensional optical processingsystem 700, in accordance with a n exemplary embodiment of theinvention.

A 2-D input (702) having N*N pixels requires a kernel having N²*N²pixels. In this case the space multiplexing may be more complex than theone in the 1-D input case. The transformation may be written as:${I_{o}\left( {k,l} \right)} = {\sum\limits_{m}{\sum\limits_{n}{{I_{in}\left( {m,n} \right)}{K\left( {m,{n;k},l} \right)}}}}$

In an exemplary embodiment, the kernel mask is divided into 2-D blocksand the index of each block will represent the output coordinate k,lwhile the location within each block m,n will represent the requiredkernel matrix. In this notation in order to perform the transformationthe input I_(in)(m,n) is replicated to each block, multiplied by thevalue of the kernel there and summed to a single value k,l in the outputplane.

In an incoherent illumination embodiment, the 2-D summation may beobtained using a lens attached to each block of the kernel, for examplea lenslet array 710. The replication of the input may be done via aDammann grating 706 or an array of prisms which are attached to theaperture of an imaging lens 704 (at 706, for example, instead of thegrating). A direction correcting prism array may be provided at areplicated image plane 708.

In an embodiment using an incoherent illumination pattern, the kernelmask may be limited to being positive since the phase information islost by the incoherence. Thus, in order to implement a generaltransformation kernel three or more parallel processing paths areoptionally used. Each pixel of the input as well of the kernel may berepresented in the following manner:I _(in)(m,n)=a ₀ ^(I)(m,n)+a ₁ ^(I)(m,n)e ^(2πi/3) +a ₂ ^(I)(m,n)e^(4πi/3)K(k,l,m,n)=a ₀ ^(K)(k,l;m,n)+a ₁ ^(K)(k,l;m,n)e ^(2πi/3) +a ₂^(K)(k,l;m,n)e ^(4πi/3)

The splitting into the three processing paths can be performed, forexample, using a Dammann grating or a prisms set attached to an imaginglens. The transformation of each path is performed and then the threepaths are summed to obtain the total output according to:$\begin{matrix}{{I_{o}\left( {k,l} \right)} = {\sum\limits_{m}{\sum\limits_{n}\left\lfloor {{{a_{0}^{I}\left( {m,n} \right)}{a_{0}^{K}\left( {k,{l;m},n} \right)}} + {{a_{1}^{I}\left( {m,n} \right)}{a_{2}^{K}\left( {m,n} \right)}} +} \right.}}} \\{\left. {{a_{2}^{I}\left( {m,n} \right)}{a_{1}^{K}\left( {m,n} \right)}} \right\rfloor + {{\mathbb{e}}^{2\quad\pi\quad{{\mathbb{i}}/2}}{\sum\limits_{m}{\sum\limits_{n}\left\lbrack {{{a_{0}^{I}\left( {m,n} \right)}{a_{1}^{K}\left( {k,{l;m},n} \right)}} +} \right.}}}} \\{\left. {{{a_{1}^{I}\left( {m,n} \right)}{a_{0}^{K}\left( {m,n} \right)}} + {{a_{2}^{I}\left( {m,n} \right)}{a_{2}^{K}\left( {m,n} \right)}}} \right\rbrack +} \\{{\mathbb{e}}^{4\quad\pi\quad{{\mathbb{i}}/3}}{\sum\limits_{m}{\sum\limits_{n}\left\lbrack {{{a_{0}^{I}\left( {m,n} \right)}{a_{2}^{K}\left( {k,{l;m},n} \right)}} + {{a_{1}^{I}\left( {m,n} \right)}{a_{1}^{K}\left( {m,n} \right)}} +} \right.}}} \\\left. {{a_{2}^{I}\left( {m,n} \right)}{a_{0}^{K}\left( {m,n} \right)}} \right\rbrack\end{matrix}$

It should be noted that within each one of the three processing pathsthree sub processing operations are applied when the most general inputrepresentation is used. For a positive input each path contains only onesub-processing path.

It is noted that instead of three spatial processing paths, one or moreof the three “paths” may be implemented by using a single system 700multiple times, one for each processing path.

For a real input/kernel an embodiment with two main processing paths canbe used: for the positive and the negative values. In this case theoutput distribution should be obtained as: $\begin{matrix}{{I_{o}\left( {k,l} \right)} = {{\sum\limits_{m}{\sum\limits_{n}\left\lbrack {{{a_{0}^{I}\left( {m,n} \right)}{a_{0}^{K}\left( {k,{l;m},n} \right)}} + {{a_{1}^{I}\left( {m,n} \right)}{a_{1}^{K}\left( {m,n} \right)}}} \right\rbrack}} -}} \\{\sum\limits_{m}{\sum\limits_{n}\left\lbrack {{{a_{0}^{I}\left( {m,n} \right)}{a_{1}^{K}\left( {k,{l;m},n} \right)}} + {{a_{1}^{I}\left( {m,n} \right)}{a_{0}^{K}\left( {m,n} \right)}}} \right\rbrack}}\end{matrix}$where a₀ represents the positive values and a₁ the negative ones.

It should be noted that the subtraction of the previous equation may beperformed by using the same detector and performing the processing intwo cycles. In the second cycle the voltage of the output detector isinverted. The first path is done in the first processing cycle and itloads the capacitor of the detector. In the second cycle the inversionstarts to unload the capacitor and thus a subtraction between the tworesults is obtained.

The present application is related to the following four PCTapplications filed on same date as the instant application in the ILreceiving office, by applicant JTC2000 Development (Delaware), Inc.:attorney docket 141/01582 which especially describes matching ofdiscrete and continuous optical elements, attorney docket 141/01541which especially describes reflective and incoherent optical processordesigns, attorney docket 141/01581 which especially describes a methodof optical sign extraction and representation, and attorney docket141/01542 which especially describes a method of processing byseparating a data set into bit-planes and/or using feedback. Thedisclosures of all of these applications are incorporated herein byreference.

It will be appreciated that the above described methods and apparatusfor optical processing may be varied in many ways, including, changingthe order of steps, which steps are performed using electricalcomponents and which steps are performed using optical components, therepresentation of the data and/or the hardware design. In addition,various distributed and/or centralized hardware configurations may beused to implement the above invention. In addition, a multiplicity ofvarious features, both of methods and of devices, have been described.It should be appreciated that different features may be combined indifferent ways. In particular, not all the features shown above in aparticular embodiment are necessary in every similar embodiment of theinvention. Further, combinations of the above features are alsoconsidered to be within the scope of some embodiments of the invention.In addition, the scope of the invention includes methods of using,constructing, calibrating and/or maintaining the apparatus describedherein. When used in the following claims, the terms “comprises”,“comprising”, “includes”, “including” or the like mean “including butnot limited to”.

1. Apparatus for optically applying a transform to data, comprising: aspatially modulated light source, that generates a spatially modulatedlight beam encoding said data by said modulation; a diffractive elementthat replicates said light beam; and a lens that applies a Fouriertransform to said replicated light beam.
 2. Apparatus according to claim1, comprising a detector that detects said transformed light. 3.Apparatus according to claim 2, comprising electronic circuitry thatconverts said detected signals into a discrete transform of said data.4. Apparatus according to claim 3, wherein said transform is a lineartransform.
 5. Apparatus according to claim 3, wherein said transform isa DCT transform.
 6. Apparatus according to claim 1, wherein saidreplicating comprises replicating said beam to a two dimensionalarrangement.
 7. Apparatus according to claim 1, wherein said diffractiveelement comprises a Dammann grating.
 8. Apparatus according to claim 1,wherein said diffractive element comprises a Ronchi grid.
 9. Apparatusaccording to claim 1, wherein said spatially modulated light encodessaid data as an array of blocks.